Problem: Solve for $x$ and $y$ using elimination. ${3x+5y = 35}$ ${3x+6y = 39}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${3x+5y = 35}$ $-3x-6y = -39$ Add the top and bottom equations together. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {3x+5y = 35}\thinspace$ to find $x$ ${3x + 5}{(4)}{= 35}$ $3x+20 = 35$ $3x+20{-20} = 35{-20}$ $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ You can also plug ${y = 4}$ into $\thinspace {3x+6y = 39}\thinspace$ and get the same answer for $x$ : ${3x + 6}{(4)}{= 39}$ ${x = 5}$